Video 2-1 Scientific Method Units of Measurement Metric Conversions.

Video 2-1

Scientific Method Units of Measurement Metric Conversions

Chapter 2

MEASUREMENT AND CALCULATIONS

I. Scientific Method

logical approach to problem solving


Basic Steps:

1. State problem (based on observations)

2. Observe and collect data (senses and instruments)

Data—recorded observations qualitative (descriptive) quantitative (numerical)


Basic Steps:3. Form hypothesis (testable statement)4. Testing

a. Experimental setup (contains variable being tested)

b. Control (identical to experimental setup EXCEPT for the variable)

c. Ideally, only one variabled. Done multiple times (for consistency)


Basic Steps:

5. Theorizing (conclusion)

a. hypotheses model theory

NOTE: Theories CANNOT turn into Laws

WHY?


Basic Steps:Theory– attempts to explain WHY a set

of conditions produce a certain result

Law– states that a certain set of conditions will always produce a certain result but DOES NOT EXPLAIN WHY.


Basic Steps:

Ex. Theory of Plate Tectonics

Ex. Law of Universal Gravitation


Basic Steps:

A scientific theory makes falsifiable predictions about things not yet observed.

A “theory” that makes no predictions that will ever be observed is not a theory.

Predictions which are not sufficiently specific to be falsified are meaningless and likewise not a scientific theory.

II. Units of Measurements

Temperature Scales:

Water oF(Fahrenheit)

oC

(Celsius)

K

(Kelvin)

Boiling pt. 212 100 373.15

Freezing pt.

32 0 273.15

Absolute Zero

-459.67 -273.15 0

180 100 100


Temperature Scales: 180 oF = 100 oC = 100 K 1.8 oF = 1 oC = 1 K


Converting between Temperature Scales: K = oC + 273.15 oF = (oC x 9/5) + 32

NOTE: You solve for the variable on the LEFT SIDE (your given quantity goes on the right side. Rearrange equations using algebra if necessary.


Converting between Temperature Scales:

Ex. Normal body temperature of humans is often described as around 98.6 oF. Determine what this is on the Celsius and Kelvin scales.


Density: mass per unit volume

D = m / V

m = D x V


Density: Units: kg / m3 (gives VERY large numbers for

dense substances; good for gases) g / cm3

g / mL


Density:

NOTE: 1 cm3 = 1 mL1 cm3 is the volume occupied by a cube that

measures 1 cm on each side.

Denser objects will sink in less dense fluids.


Density:

Ex. An object is placed into a graduated cylinder with 35.3 mL of water. After the object sinks, the volume of the water rises to 46.8 mL. If the object’s density is 2.47 g/cm3, what is the mass of the object?


Density:

Ex. Why will a 10.0 gram ball of clay sink if placed into a tray of water, but float if the clay is flattened out into the shape of a boat? NOTE: The density of water is 1.00 g/mL.

IV. Metric Conversion

Kids Have Dropped over dead converting metrics

2.45 hg = g

K H D o d c m

START

END

245.

ILO

ECTA

EKA

eci

enti

illi



8.3 mm = dam

K H D o d c m

STARTEND

0 0 0 .00083



mega (M) = 106 micro () = 10-6

giga (G) = 109 nano (n) = 10-9

tera (T) = 1012 pico (p) = 10-12

T _ _ G _ _ M _ _ K H D o d c m _ _ _ _ n _ _ p

Video 2-2

Scientific Notation Significant Figures Math and Sigfigs Percent Error

VII. Scientific Notation

value is expressed in the form:

a.bbb x 10y

where a.bbb must be between 1 and 10


Ex. Write the following in scientific notation:

5203.04 = 5.20304 x 103

0.000254= 2.54 x 10-4

102.56 x 102

= 1.0256 x 104

2.5498= 2.5498 x 100


Use your calculator to convert standard notation into scientific notation

Look for the “sci” mode (varies with calculators)

VIII. Significant Figures

Significant figures: all the numbers in a measurement that can be known precisely plus a last digit that must be estimated.

All the numbers you are sure of plus one more decimal place (estimated).


Rules for determining HOW MANY SIGFIGS in a measurement:

1) Count all nonzero digits (no matter is before or after decimal).

Ex. 584.39 g

2) Count all zeros between nonzero numbers.

Ex. 4300.002308 mL



3) Do NOT count zeros in front of nonzero digits (place holders).

Ex. 0.000546902 kg



4) Count zeros at the END of a number ONLY if the number contains a decimal point. If there is no decimal point, the zeros are UNCERTAIN.

Ex. 4950.87000 mm 678900 L


Ex. Determine how many sigfigs are in each of the following measurements:

354.2 g 32.0305 mL 0.00254 km 0.34050 mm 235000 hL

46

3

5

?


When rounding off a number to a specific number of sigfigs: Find the LAST sigfig in the number and look at

the number AFTER it. If it is 5 or greater, round the last sigfig up (ignore book rules). If it is less than five, drop all digits after the last sigfig.

NOTE: When converting a measurement to scientific notation, the number of sigfigs MUST be the same as in the original measurement.


Ex. Round off the following numbers to the indicated number of sigfigs and rewrite the answer in scientific notation.

measurement No. of sigfigs Answer Scientific Notation

5247.23 g 5

96742.35 m 3

0.045038 L 1

24.85 x 106 g 2

5247.2 g 5.2472 x 103 g

96700 m 9.67 x 104 m

0.05 L 5 x 10-2 L

25 x 106 g 2.5 x 107 g

IX. Mathematical Operations with Sigfigs

Addition or Subtraction: The answer must have the same number of

DECIMAL PLACES as the measurement with the LEAST number of decimal places.


Ex. Answer the following with the correct number of sigfigs:

563.02 + 12.027 =

1002.5 + 0.254831 =

500 – 6.842 + 24.51 =

575.047 = 575.05

1002.754831 = 1002.8

517.668 = 518


Multiplication or Division: The answer cannot have more sigfigs than the

measurement with the LEAST total number of sigfigs.



563.02 ÷ 12.02 =

10.05 x 0.254 =

508 ÷ 6.842 x 24.51 =

46.8402662 = 46.84

2.5527 = 2.55

1819.801228 = 1.82 x 103


For all operations, perform ALL similar operations (+ and – are similar; x and are similar) FIRST, then round off to the proper number of sigfigs. Do NOT round off after each calculation



563.02 x 12.02 / 21.3 =

10.05 + 0.254 – 6.2 =

317.7230235 = 318

4.104 = 4.1


If there is a mixture of operations, round off before going to a “dissimilar” operation. Use the rules for the last operation you just did.



(563.02 ÷ 12.02) + 3.2 = 46.8402662 + 3.2

= 46.84 + 3.2 = 50.04 = 50.0



(563.02 + 12.8) x 3.2 / 5.408 =

575.82 x 3.2 / 5.408

= 340.7100592 = 340 = 3.4 x 102

= 575.8 x 3.2 / 5.408

X. Calculating Percent Error

Percent error

% error =

can have a positive or negative value Less than 5% error (for small values)

Valueaccepted - Valueexperimental

Valueaccepted X 100%

Video 2-3

Graphing Data and Numerical Relationships

XI. Graphing Data and Numerical Relationships

Directly proportional quantities: y/x = a constant y = kx where k is the slope straight line


X

Y

..

..

..

. .


Inversely proportional quantities: xy = a constant y = k/x hyperbola


X

Y

.

.

..

. . .


GRAPHING DATA: Often, you will have to graph data that you

measured. In experimental sciences, there are two types of variables:


1. Independent variables—a variable that YOU can determine, manipulate, vary, control, etc.

2. Dependent variable—a variable that CHANGES (or is determined) by your actions or input.


X-axis: independent axis (variable) Y-axis: dependent axis (variable) Graphing is ALWAYS the dependent vs. independent variable (y vs. x)


Time (seconds)

Temperature (oC)

Temperature vs. Time

Video 2-4

Dimensional Analysis Derived Units Problem Solving Strategies

XII. Dimensional Analysis

When CONVERTING a measurement between one system of units to another, simply do this:

Given Quantity (units) Xunits getting rid of

new unitsnumber

number


When CONVERTING a measurement between one system of units to another, simply do this:

Given Quantity (units) Xunits getting rid of

new unitsnumber

number

CONVERSION FACTOR


Conversion factor is simply (and ALWAYS) a fraction that is equal to 1

Numerator is equivalent to the denominator Use EQUALITIES


Examples:

1 ft = 12 inches 2.205 lbs = 1 kg1 hr = 3600 sec 1000 m = 1 km

NOTE: the 1 ft, 1 kg, 1 km, 1 hr in these equalities are EXACT (defining) quantities and have an INFINITE number of sigfigs (values are 1.000000000000000 . . .)


Examples:

How many pounds are in 9.8 kg?

9.8 kg xkg

lbs2.205

1

= 21.609 lbs = 22 lbs


Examples:

If 1 inch is equivalent to 2.54 cm, how many inches are in 2.50 m?

2.50 m xm

cm

1 inch = 2.54 cm

1

100x

cm

in

2.54

1

= 98.42519685 in = 98.4 in

III. Derived Units

units that are obtained by multiplying or dividing standard units: Ex. volume = length (m) x width (m) x height (m) V = m x m x m = m3

Finding equivalent units:

III. Derived Units


1 m3 = ? cm3

1 m = 100 cm

(1 m)3 = (100 cm)3

1 m3 = 1,000,000 cm3 = 1 x 106 cm3

III. Derived Units


Ex. How many square feet are equivalent to a square meter? 1 meter = 3.28 feet

XIII. Problem Solving Strategies

The problems facing you in this class will fall into one of the following categories:

1. Conversion (changing a measurement to a different unit)

2. Formula (changing one type of measurement to a different TYPE of measurement)


Often, you will need to do both things. So, first, determine which formula you need to

use (rearrange the formula for the unknown)

second, convert any given quantities into the proper units if necessary

third, plug the values in and calculate


What are some terms that mean: Equals Add Subtract Multiply Divide

Video 2-5

Measuring Techniques Accuracy and Precision

V. MEASURING TECHNIQUES

A measurement is a comparison against a STANDARD UNIT.

3 Standard types of measurements: Mass (the amount of matter present in

something) Volume (the amount of space something takes

up) Length (the distance from one part of the object

to another part)


Standard units (Metric System)

Length: Meter (millimeter, centimeter, kilometer)

Volume: Liter (milliliter, cubic centimeter) Mass: Kilogram (gram, milligram)


MAKING MEASUREMENTS:

1) Determine the value of the SMALLEST unit (line) that the instrument will measure.


Meter stick (ruler):

1 line = 1 millimeter = 0.1 centimeters


Electronic Balance (mass):

No lines (digital display)


Graduated cylinder (volume): varies with capacity of the cylinder


2) Use proper techniques for measuring: Rulers: Do NOT start measuring from the

beginning of the ruler. Start from the 1 centimeter (10 millimeter) mark. SUBTRACT 1 cm (or 10 mm) from your measurement.


2) Use proper techniques for measuring: Balance: Record reading after it has

stabilized (check and include units)


2) Use proper techniques for measuring: Graduated cylinder: Make sure the

meniscus (curve of fluid) is at eye level. Read the BOTTOM of the meniscus.


3) Estimating decimal places. Make sure you ESTIMATE one more

decimal place to the right. If the instrument reads to the 0.1, estimate to the 0.01 place.


3) Estimating decimal places.


4) Filling a cylinder to a specific volume. Use a beaker and dropper to fill a

GRADUATED CYLINDER.


5) Electronic Balance: Tare (or Zero) button will set reading

to 0.00 g (ignores any mass on balance)

Do NOT estimate an extra decimal place (last digit is already an estimate).


5) Electronic Balance:


6) Choosing the correct piece of lab equipment:

When should you use a Beaker?



When should you use a Beaker? Holding liquid (easy to pour) Mixing liquid with stirring rod Heating liquid NOT for measuring volume



When should you use a Erlenmeyer flask?



When should you use a Erlenmeyer flask? Mixing (swirling) liquid Heating liquid NOT for pouring NOT for measuring volume



When should you use a Graduated cylinder?



When should you use a Graduated cylinder? Measuring volumes accurately NOT for heating NOT for storing large quantities



When should you use a Pipet?



When should you use a Pipet? TRANSFERRING a precise amount of

liquid



When should you use a Buret?



When should you use a Buret? When you DON’T know how much of a

liquid you will need Transferring precise amounts of liquid.



What size should you use?

Smallest size possible that will “get the job done” (measure quantities without being refilled).

VI. Accuracy and Precision

Accuracy: the closeness of measurements to the correct or accepted value of the measured quantity.

Precision: the reproducibility of a set of measurements made in the same way.

Significant figures (sigfigs) reflect the precision of a measurement.


Neither accurate nor precise


Precise


Both accurate and precise


Examples: One students measures the length of an

object to be 10.2 cm. The actual length is 10.8 cm. Is his measurement accurate? Precise?




% error = (10.8 – 10.2) / 10.8 x 100

= 5.56 %




To determine if it is precise, more measurements are needed.




He measures it 3 more times. Values are 10.7 cm, 11.4 cm, and 10.9 cm.




NOT precise. But, the average of his 4 measurements is 10.8 cm.

Improved ACCURACY


Why is his precision poor? What do the markings on his ruler look like? Remember the rules for measuring

One more decimal place than the ruler can read to.

Ruler’s smallest marking are 1 cm


Why is his precision poor? If the marking are worth 0.1 cm he can

better estimate the measurement (sure of the 0.1 cm, estimate the 0.01 cm place).

Measurements should be REPRODUCIBLE to the 0.1 cm

Does NOT mean they will be accurate

Video 2-1 Scientific Method Units of Measurement Metric Conversions.

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Transcript of Video 2-1 Scientific Method Units of Measurement Metric Conversions.